It was announced on Monday that pop star Nicole Scherzinger, 32, will officially be replacing Cole, 27, as a judge on the new US version of the X Factor.
When Geordie Cheryl's exit from the talent competition was first reported, rumours of a feud - or lack of chemistry - between her and fellow judge Abdul began to circulate.
But the 48-year-old took to her Twitter page yesterday to address Cole's departure.
She wrote: 'Cheryl is amazing. We have forged a wonderful friendship & have been & will continue to stay in touch.
'I'm excited for everyone to see and hear what she is about to do next.'